I'm still trying to figure out how to stay fit in Bangalore. There are a fair number of gyms here - which is definitely an option. However, the avenues for playing any sports are limited.
Minus the past week and a half when I've been sick, I have been going to the climbing wall at kanteerava stadium. It's pretty cool and there are a bunch of friendly climbers there around 7-9am and 4-6pm.
We investigated most of the clubs in Bangalore looking for squash, tennis, badminton, swimming... but most of them have huge membership initiation fees and 15-20 year waiting lists.
I'm looking at playing/learning tennis at the Karnataka State Lawn Tennis Association (KSLTA) which has a few courts, good gym, clean locker rooms, a reasonable fee, and no waiting list. The only downside is that you have to sign up for a 3 year membership and, never having played much tennis, that's a big commitment (esp. since it only has tennis and no other sports).